Coral Holobiont Physiology under OA/OW

Model selection for physiology

Physiological response parameters were assessed using mixed-effects linear models across species and treatments. Model selection was carried out using backward elimination of random-effects followed by fixed-effects using the package lmerTest (version 3.1.3)

Protein

While value ~ species + fpco2 + ftemp + (1 | colony) + species:ftemp was the best-fit model structure identified, we wanted to model both pCO₂ and temperature responses by species so moving forward we are using the following model structure:

value ~ species * (fpco2 + ftemp) + (1 | colony)

Figure:

Carbohydrate

While value ~ species + ftemp was the best-fit model structure identified, we wanted to model responses with a random effect of colony so moving forward we are using the following model structure:

value ~ species * (fpco2 + ftemp) + (1 | colony)

Figure:

Lipid

While value ~ species + ftemp + reef + species:ftemp + species:reef was the best-fit model structure identified, we wanted to model both pCO₂ and temperature responses by species and with random effect of colony so moving forward we are using the following model structure:

value ~ species * (fpco2 + ftemp) + reef + species:reef + (1 | colony)

Figure:

Density

While value ~ species + fpco2 + ftemp + reef + (1 | colony) + species:fpco2 + species:ftemp + fpco2:ftemp + species:reef + fpco2:reef + ftemp:reef + species:fpco2:ftemp + species:fpco2:reef + species:ftemp:reef + fpco2:ftemp:reef + species:fpco2:ftemp:reef was the best-fit model structure identified, we wanted to model both pCO₂ and temperature responses by species and with random effect of colony so moving forward we are using the following model structure:

value ~ species * (fpco2 + ftemp) + reef + species:reef + (1 | colony)

Figure:

Chlorophyll

Since the best-fit model fits our design, we will proceed with the following model structure:

value ~ species + fpco2 + ftemp + reef + (1 | colony) + species:fpco2 + species:ftemp + fpco2:ftemp + species:reef

Figure:

Total Host

Since the best-fit model fits our design, we will proceed with the following model structure:

value ~ species + fpco2 + ftemp + reef + (1 | colony) + species:fpco2 + species:ftemp + species:reef + fpco2:reef + species:fpco2:reef

Figure:

Calcification

This is the same model from Bove et al 2019, just matching aesthetics for this manuscript.

Figure 1

Figure 1. Modeled 95% confidence interval of (A) total host energy reserves (mg cm^-2), (B) cell density (10⁶ cells cm^-2), and (C) Chlorophyll a (ug cm^-2) for S. siderea, P. strigosa, and P. astreoides at T0 (green) or T90 (red/blue), with individual coral fragment physiology denoted by points. Blue denotes 28°C and red denotes 31°C, with pCO₂ treatment along the x axis.

Correlation assessments

Here, I am exploring the relationships between each physiology parameter measured above.

Figure 2. Correlation matrix for S. siderea, P. strigosa, and P. astreoides depicting pair-wise comparisons of physiological parameters within each species. Colour and ellipse width denote R² of each significant comparison, and blank grids represent non-significant pair-wise comparisons (P > 0.05).Each parameter is denoted in blue text along the diagonal of each plot. Correlations with R² above 0.5 (shown in orange and red in matrix plot) are explored further below.

Siderastrea siderea

Pseudodiploria strigosa

Porites astreoides

Holobiont PCAs

Siderastrea siderea

## 
## Call:
## adonis(formula = value ~ reef + ftemp + fpco2, data = s_df_l,      method = "eu") 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##            Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)  
## reef        1       544   544.0  0.3565 0.00068  0.553  
## ftemp       1      3538  3537.7  2.3184 0.00443  0.146  
## fpco2       3     15517  5172.4  3.3897 0.01945  0.015 *
## Residuals 510    778211  1525.9         0.97543         
## Total     515    797810                 1.00000         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Pseudodiploria strigosa

## 
## Call:
## adonis(formula = value ~ reef + ftemp + fpco2, data = p_df_l,      method = "eu") 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##            Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)  
## reef        1     10809 10809.2  3.4558 0.00709  0.067 .
## ftemp       1     18776 18775.5  6.0027 0.01231  0.012 *
## fpco2       3     31998 10666.2  3.4100 0.02098  0.021 *
## Residuals 468   1463839  3127.9         0.95963         
## Total     473   1525422                 1.00000         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Porites astreoides

## 
## Call:
## adonis(formula = value ~ reef + ftemp + fpco2, data = a_df_l,      method = "eu") 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##            Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)  
## reef        1        78    78.2  0.0742 0.00018  0.789  
## ftemp       1      5023  5023.4  4.7659 0.01140  0.023 *
## fpco2       3     11786  3928.7  3.7273 0.02675  0.012 *
## Residuals 402    423715  1054.0         0.96167         
## Total     407    440603                 1.00000         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Figure 2

Plasticity analyses

Questions to ask:

• What should I use as a loading in my PCA?
• Calculating distance from T0/control mean or from colony value?
• What about duplicate samples from same colony per treatment or from same sample?
• What about samples that don’t have a T0 or control fragment? Should I be comparing within colony or within T0/control?
• I think I am going to model the responses so that colony is being considered. Thoughts?

Control Comparison (400 \(\mu\)atm; 28 °C)

S. siderea

aov(distance ~ pCO2 * temperature * reef)

##                  Df Sum Sq Mean Sq F value   Pr(>F)    
## fpco2             3  52.34  17.447  12.398 1.36e-06 ***
## ftemp             1   4.62   4.620   3.283 0.074304 .  
## reef              1  17.19  17.194  12.218 0.000826 ***
## fpco2:ftemp       3  19.90   6.635   4.715 0.004696 ** 
## fpco2:reef        3  10.08   3.361   2.388 0.076194 .  
## ftemp:reef        1   0.68   0.679   0.482 0.489638    
## fpco2:ftemp:reef  3   4.93   1.643   1.168 0.328330    
## Residuals        70  98.51   1.407                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Reef environment:

##           diff       lwr       upr        p adj
## N-F -0.8918785 -1.402693 -0.381064 0.0008610358

Temperature:

##            diff         lwr       upr      p adj
## 31-28 0.4629949 -0.04781959 0.9738094 0.07494486

pCO₂:

##                 diff         lwr         upr        p adj
## 420-300  -1.04810665 -2.05630773 -0.03990557 3.852069e-02
## 680-300  -0.09048749 -1.08908913  0.90811415 9.951844e-01
## 3300-300  1.07998914  0.09026878  2.06970950 2.705280e-02
## 680-420   0.95761916  0.02655061  1.88868771 4.147164e-02
## 3300-420  2.12809579  1.20655914  3.04963244 3.394696e-07
## 3300-680  1.17047663  0.25945215  2.08150111 6.360085e-03

---

P. strigosa

aov(distance ~ pCO2 + temperature + reef + pCO2:temperature)

##             Df Sum Sq Mean Sq F value Pr(>F)  
## fpco2        3  11.91   3.971   2.066 0.1126  
## ftemp        1   3.54   3.539   1.841 0.1792  
## reef         1   3.00   2.999   1.560 0.2158  
## fpco2:ftemp  3  22.06   7.353   3.825 0.0135 *
## Residuals   70 134.57   1.922                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Reef environment:

##          diff        lwr      upr     p adj
## N-F 0.3966685 -0.2371093 1.030446 0.2160887

Temperature:

##            diff        lwr      upr     p adj
## 31-28 0.4365546 -0.2089166 1.082026 0.1817144

pCO₂:

##               diff        lwr        upr      p adj
## 420-300  -1.268832 -2.6342004 0.09653637 0.07787008
## 680-300  -0.186533 -1.2666855 0.89361956 0.96853921
## 3300-300 -0.318319 -1.3726392 0.73600121 0.85665896
## 680-420   1.082299 -0.3197300 2.48432814 0.18635502
## 3300-420  0.950513 -0.4317124 2.33273847 0.27742695
## 3300-680 -0.131786 -1.2331696 0.96959758 0.98909261

---

P. astreoides

aov(distance ~ pCO2 + temperature + reef)

##             Df Sum Sq Mean Sq F value   Pr(>F)    
## fpco2        3  32.12  10.707   7.776 0.000173 ***
## ftemp        1   9.68   9.676   7.027 0.010177 *  
## reef         1   1.35   1.353   0.983 0.325427    
## Residuals   62  85.37   1.377                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Reef environment:

##          diff        lwr       upr     p adj
## N-F 0.2780969 -0.2947748 0.8509686 0.3356237

Temperature:

##            diff       lwr      upr      p adj
## 31-28 0.7811527 0.1859322 1.376373 0.01094389

pCO₂:

##                 diff        lwr        upr        p adj
## 420-300  -1.36493076 -2.4275070 -0.3023545 0.0065068409
## 680-300   0.01915618 -1.0285582  1.0668705 0.9999591525
## 3300-300  0.48643513 -0.5926162  1.5654864 0.6353107458
## 680-420   1.38408693  0.3363726  2.4318013 0.0048748389
## 3300-420  1.85136589  0.7723146  2.9304172 0.0001582493
## 3300-680  0.46727895 -0.5971405  1.5316984 0.6546745575

---

T0 Comparison

S. siderea

## 
## Call:
## adonis(formula = value ~ treat2, data = s_plast_l, method = "eu") 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##            Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)  
## treat2      8     28005  3500.6  2.1277 0.03488  0.034 *
## Residuals 471    774911  1645.2         0.96512         
## Total     479    802916                 1.00000         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##             Df Sum Sq Mean Sq F value   Pr(>F)    
## treat2       8  44.96   5.620   4.859 5.79e-05 ***
## reef         1   3.94   3.937   3.404   0.0685 .  
## Residuals   86  99.47   1.157                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

P. strigosa

## 
## Call:
## adonis(formula = value ~ treat2, data = p_plast_l, method = "eu") 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##            Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)  
## treat2      8     65917  8239.6   2.384 0.04285  0.023 *
## Residuals 426   1472357  3456.2         0.95715         
## Total     434   1538274                 1.00000         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##             Df Sum Sq Mean Sq F value  Pr(>F)   
## treat2       8  31.61   3.951   3.491 0.00173 **
## reef         1   9.92   9.916   8.763 0.00408 **
## Residuals   77  87.13   1.132                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

P. astreoides

## 
## Call:
## adonis(formula = value ~ treat2, data = a_plast_l, method = "eu") 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##            Df SumsOfSqs MeanSqs F.Model    R2 Pr(>F)   
## treat2      8     32081  4010.1  3.6221 0.069  0.002 **
## Residuals 391    432883  1107.1         0.931          
## Total     399    464964                 1.000          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##             Df Sum Sq Mean Sq F value   Pr(>F)    
## treat2       8  83.07  10.384   12.94 3.03e-11 ***
## reef         1   8.66   8.656   10.78   0.0016 ** 
## Residuals   70  56.19   0.803                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Supplemental Tables

Table 1. T90 modeled mean coral host protein content and 95% confidence intervals for each species

treatment	N	mean	lower 95%	upper 95%
(a) SSID
288_28	11	0.49	0.40	0.57
311_31	9	0.44	0.35	0.52
3285_28	12	0.45	0.37	0.53
3309_31	12	0.39	0.31	0.47
405_31	12	0.46	0.38	0.54
447_28	12	0.52	0.44	0.60
673_28	13	0.47	0.38	0.54
701_31	12	0.41	0.33	0.49
(b) PSTR
288_28	16	0.56	0.49	0.64
311_31	9	0.32	0.23	0.41
3285_28	16	0.42	0.34	0.50
3309_31	8	0.17	0.08	0.27
405_31	6	0.18	0.07	0.29
447_28	5	0.42	0.30	0.54
673_28	14	0.45	0.37	0.53
701_31	7	0.21	0.11	0.31
(c) PAST
288_28	11	0.24	0.15	0.33
311_31	6	0.19	0.08	0.29
3285_28	12	0.11	0.02	0.20
3309_31	4	0.06	-0.05	0.17
405_31	7	0.16	0.07	0.27
447_28	12	0.21	0.12	0.30
673_28	10	0.15	0.06	0.25
701_31	9	0.11	0.01	0.20

Table 2. T90 modeled mean coral host lipid content and 95% confidence intervals for each species

treatment	N	mean	lower 95%	upper 95%
(a) SSID
288_28	11	0.40	0.29	0.50
311_31	9	0.37	0.26	0.48
3285_28	12	0.37	0.27	0.47
3309_31	12	0.35	0.25	0.45
405_31	12	0.38	0.29	0.48
447_28	12	0.41	0.30	0.51
673_28	13	0.33	0.23	0.43
701_31	12	0.31	0.21	0.41
(b) PSTR
288_28	16	0.27	0.18	0.37
311_31	9	0.14	0.02	0.24
3285_28	15	0.22	0.12	0.32
3309_31	8	0.08	-0.04	0.19
405_31	5	0.12	-0.03	0.26
447_28	5	0.26	0.11	0.40
673_28	14	0.22	0.11	0.32
701_31	7	0.07	-0.04	0.20
(c) PAST
288_28	11	0.21	0.10	0.33
311_31	6	0.26	0.13	0.38
3285_28	12	0.13	0.01	0.24
3309_31	4	0.20	0.07	0.33
405_31	7	0.22	0.10	0.34
447_28	12	0.17	0.06	0.27
673_28	10	0.11	0.01	0.23
701_31	9	0.16	0.05	0.28

Table 3. T90 modeled mean coral host carbohydrate content and 95% confidence intervals for each species

treatment	N	mean	lower 95%	upper 95%
(a) SSID
288_28	11	1.15	0.95	1.35
311_31	8	0.82	0.61	1.02
3285_28	12	1.10	0.91	1.29
3309_31	12	0.77	0.60	0.96
405_31	12	0.75	0.57	0.94
447_28	12	1.08	0.90	1.26
673_28	13	1.27	1.10	1.45
701_31	12	0.94	0.75	1.11
(b) PSTR
288_28	16	0.77	0.60	0.93
311_31	9	0.50	0.30	0.68
3285_28	16	0.62	0.45	0.78
3309_31	8	0.34	0.15	0.55
405_31	6	0.40	0.16	0.65
447_28	5	0.67	0.41	0.92
673_28	14	0.56	0.37	0.75
701_31	7	0.29	0.07	0.51
(c) PAST
288_28	11	0.82	0.61	1.03
311_31	6	0.65	0.41	0.88
3285_28	12	0.58	0.38	0.78
3309_31	4	0.41	0.16	0.65
405_31	7	0.73	0.51	0.95
447_28	12	0.90	0.71	1.10
673_28	10	0.61	0.41	0.81
701_31	9	0.43	0.23	0.64

Table 4. T90 modeled mean algal endosymbiont cell density and 95% confidence intervals for each species

treatment	N	mean	lower 95%	upper 95%
(a) SSID
288_28	11	3.32	2.23	4.46
311_31	9	2.45	1.33	3.58
3285_28	12	2.04	0.97	3.07
3309_31	12	1.18	0.12	2.23
405_31	12	2.61	1.55	3.67
447_28	12	3.48	2.42	4.50
673_28	13	2.96	1.95	3.98
701_31	12	2.10	1.04	3.14
(b) PSTR
288_28	16	2.16	1.14	3.15
311_31	9	0.42	-0.77	1.60
3285_28	16	1.53	0.53	2.52
3309_31	8	-0.27	-1.48	0.89
405_31	6	0.45	-0.96	1.86
447_28	5	2.16	0.75	3.61
673_28	14	1.71	0.68	2.75
701_31	7	-0.09	-1.30	1.14
(c) PAST
288_28	11	7.29	6.13	8.48
311_31	6	6.42	5.02	7.74
3285_28	12	5.92	4.74	7.16
3309_31	4	4.86	3.51	6.15
405_31	6	5.51	4.22	6.83
447_28	12	6.43	5.28	7.57
673_28	10	5.09	3.84	6.35
701_31	8	4.19	2.87	5.45

Table 5. T90 modeled mean algal endosymbiont chlorophyll a content and 95% confichlace intervals for each species

treatment	N	mean	lower 95%	upper 95%
(a) SSID
288_28	11	111.62	79.83	142.93
311_31	9	105.32	71.66	138.94
3285_28	12	48.77	17.98	79.06
3309_31	12	32.88	2.52	62.85
405_31	12	78.09	46.98	108.90
447_28	12	155.02	123.15	185.60
673_28	13	83.80	54.26	112.09
701_31	12	82.13	52.64	112.24
(b) PSTR
288_28	16	186.56	157.46	214.70
311_31	9	120.87	86.12	156.21
3285_28	16	78.92	50.45	107.95
3309_31	8	-1.60	-37.38	34.54
405_31	6	26.31	-13.62	66.76
447_28	5	161.10	118.69	203.66
673_28	14	83.70	54.83	112.50
701_31	7	17.80	-17.46	55.99
(c) PAST
288_28	11	96.99	64.84	130.13
311_31	6	155.80	116.69	193.74
3285_28	12	15.60	-16.92	47.45
3309_31	4	61.57	19.84	101.90
405_31	7	52.42	15.21	88.19
447_28	12	64.58	33.39	95.25
673_28	10	33.03	-0.94	66.96
701_31	9	95.56	61.63	129.07

Table 6. Total coral host physiology at T90 modeled mean and 95% confidence intervals for each physiological parameter per species

treatment	N	mean	lower 95%	upper 95%
(a) SSID
288_28	11	2.02	1.62	2.42
311_31	8	1.62	1.21	2.03
3285_28	12	1.92	1.56	2.28
3309_31	12	1.53	1.18	1.88
405_31	12	1.58	1.21	1.95
447_28	12	2.03	1.66	2.40
673_28	13	2.06	1.71	2.42
701_31	12	1.66	1.29	2.01
(b) PSTR
288_28	16	1.59	1.25	1.93
311_31	9	0.96	0.58	1.33
3285_28	15	1.27	0.90	1.62
3309_31	8	0.60	0.22	0.98
405_31	5	0.71	0.17	1.27
447_28	5	1.38	0.83	1.95
673_28	14	1.23	0.86	1.62
701_31	7	0.56	0.16	0.97
(c) PAST
288_28	11	1.26	0.83	1.68
311_31	6	1.12	0.66	1.58
3285_28	12	0.86	0.42	1.30
3309_31	4	0.56	0.14	0.97
405_31	7	1.13	0.71	1.56
447_28	12	1.26	0.85	1.67
673_28	10	0.85	0.43	1.27
701_31	9	0.73	0.31	1.14

## Note: zip::zip() is deprecated, please use zip::zipr() instead

Session information

Session information from the last run date on 2020-11-17:

## R version 3.5.1 (2018-07-02)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS High Sierra 10.13.6
## 
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] grid      stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] wesanderson_0.3.6  RColorBrewer_1.1-2 gridGraphics_0.5-0
##  [4] corrplot_0.84      Hmisc_4.2-0        Formula_1.2-3     
##  [7] survival_2.44-1.1  magick_2.2         ggpubr_0.2.4      
## [10] magrittr_1.5       vroom_1.2.0        lmerTest_3.1-3    
## [13] lme4_1.1-21        Matrix_1.2-17      kableExtra_1.1.0  
## [16] ggfortify_0.4.7    cowplot_1.0.0      Rmisc_1.5         
## [19] shiny_1.4.0        vegan_2.5-5        lattice_0.20-41   
## [22] permute_0.9-5      forcats_0.4.0      stringr_1.4.0     
## [25] purrr_0.3.3        tibble_2.1.3       tidyverse_1.3.0   
## [28] plotly_4.9.0       openxlsx_4.1.2     tidyr_1.0.0       
## [31] ggbiplot_0.55      scales_1.1.0       plyr_1.8.5        
## [34] dplyr_0.8.3        ggplot2_3.2.1      readr_1.3.1       
## [37] knitr_1.25        
## 
## loaded via a namespace (and not attached):
##  [1] minqa_1.2.4         colorspace_1.4-1    ggsignif_0.6.0     
##  [4] ellipsis_0.3.0      htmlTable_1.13.1    base64enc_0.1-3    
##  [7] fs_1.3.1            rstudioapi_0.10     farver_2.0.1       
## [10] ggrepel_0.8.1       bit64_0.9-7         fansi_0.4.1        
## [13] lubridate_1.7.4     xml2_1.2.2          splines_3.5.1      
## [16] jsonlite_1.6        nloptr_1.2.1        broom_0.5.2        
## [19] cluster_2.1.0       dbplyr_1.4.2        compiler_3.5.1     
## [22] httr_1.4.1          backports_1.1.5     assertthat_0.2.1   
## [25] fastmap_1.0.1       lazyeval_0.2.2      cli_2.0.1          
## [28] later_1.0.0         acepack_1.4.1       htmltools_0.4.0    
## [31] tools_3.5.1         gtable_0.3.0        glue_1.3.1         
## [34] Rcpp_1.0.3          cellranger_1.1.0    vctrs_0.2.4        
## [37] nlme_3.1-140        xfun_0.8            rvest_0.3.5        
## [40] mime_0.7            lifecycle_0.2.0     MASS_7.3-51.4      
## [43] hms_0.5.3           promises_1.1.0      parallel_3.5.1     
## [46] yaml_2.2.0          gridExtra_2.3       rpart_4.1-15       
## [49] latticeExtra_0.6-28 stringi_1.4.5       highr_0.8          
## [52] checkmate_1.9.4     boot_1.3-23         zip_2.0.3          
## [55] rlang_0.4.5         pkgconfig_2.0.3     evaluate_0.14      
## [58] labeling_0.3        htmlwidgets_1.3     bit_1.1-14         
## [61] tidyselect_1.0.0    R6_2.4.1            generics_0.0.2     
## [64] DBI_1.0.0           pillar_1.4.3        haven_2.2.0        
## [67] foreign_0.8-71      withr_2.1.2         mgcv_1.8-28        
## [70] nnet_7.3-12         modelr_0.1.5        crayon_1.3.4       
## [73] rmarkdown_1.16      readxl_1.3.1        data.table_1.12.2  
## [76] reprex_0.3.0        digest_0.6.23       webshot_0.5.1      
## [79] xtable_1.8-4        httpuv_1.5.2        numDeriv_2016.8-1.1
## [82] munsell_0.5.0       viridisLite_0.3.0